"Your coffee has become cold because you were speaking."
Translation:bIrchoHpu' qa'vInlIj bIjatlhtaHmo'.
Yes, subordinate clauses can appear on either side of the main clause. The Duolingo course doesn't always let you do that, on the theory that it was presented to you in a certain order in one language, so it should appear in the same order in the other language. But when writing your own, original sentences, you can go either way. Any clauses with the verb suffixes -chugh, -DI', -mo', pa', or -vIS may appear on either side of the main clause.
Notice, however, that purpose clauses (those with -meH on the verb) can only come before the verb or noun they're modifying.